Abstract

Studies aimed at understanding the global properties of the hyperpolarizabilities have focused on identifying universal properties when the hyperpolarizabilities are at the fundamental limit. These studies have taken two complimentary approaches: (1) Monte Carlo techniques that statistically probe the full parameter space of the Schrödinger equation using the sum rules as a constraint, and (2) numerical optimization studies of the first and second hyperpolarizability where models of the scalar and vector potentials are parameterized and the optimized parameters determined, from which universal properties are investigated. Here, we employ an energy spectrum constraint on the Monte Carlo method to bridge the divide between these two approaches. The results suggest an explanation for the origin of the factor of the 20–30 gap between the best molecules and the fundamental limits and establish the basis for the three-level ansatz.

© 2011 Optical Society of America

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  1. M. G. Kuzyk, “Physical limits on electronic nonlinear molecular susceptibilities,” Phys. Rev. Lett. 85, 1218–1221 (2000).
    [CrossRef] [PubMed]
  2. M. G. Kuzyk, “Fundamental limits on third-order molecular susceptibilities,” Opt. Lett. 25, 1183–1185 (2000).
    [CrossRef]
  3. M. G. Kuzyk, “Quantum limits of the hyper-Rayleigh scattering susceptibility,” IEEE J. Sel. Top. Quantum Electron. 7, 774–780(2001).
    [CrossRef]
  4. M. G. Kuzyk, “Errata,” Opt. Lett. 28, 135–135 (2003).
    [CrossRef]
  5. M. G. Kuzyk, “Errata,” Phys. Rev. Lett. 90, 039902 (2003).
    [CrossRef]
  6. K. Tripathy, J. Pérez-Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945(2004).
    [CrossRef] [PubMed]
  7. K. Tripathy, J. J. Pérez-Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Errata,” J. Chem. Phys. 125, 079905 (2006).
    [CrossRef]
  8. A. D. Slepkov, F. A. Hegmann, S. Eisler, E. Elliot, and R. R. Tykwinski, “The surprising nonlinear optical properties of conjugated polyyne oligomers,” J. Chem. Phys. 120, 6807–6810(2004).
    [CrossRef] [PubMed]
  9. J. C. May, J. H. Lim, I. Biaggio, N. N. P. Moonen, T. Michinobu, and F. Diederich, “Highly efficient third-order optical nonlinearities in donor-substituted cyanoethynylethene molecules,” Opt. Lett. 30, 3057–3059 (2005).
    [CrossRef] [PubMed]
  10. J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
    [CrossRef]
  11. Q. Y. Chen, L. Kuang, Z. Y. Wang, and E. H. Sargent, “Cross-linked C-60 polymer breaches the quantum gap,” Nano Lett. 4, 1673–1675 (2004).
    [CrossRef]
  12. J. Zhou and M. G. Kuzyk, “Intrinsic hyperpolarizabilities as a figure of merit for electro-optic molecules,” J. Phys. Chem. C 112, 7978–7982 (2008).
    [CrossRef]
  13. M. G. Kuzyk, “Using fundamental principles to understand and optimize nonlinear-optical materials,” J. Mater. Chem. 19, 7444–7465 (2009).
    [CrossRef]
  14. H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem. Int. Ed. 44, 7922–7925 (2005).
    [CrossRef]
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    [CrossRef] [PubMed]
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  19. J. Pérez-Moreno and M. G. Kuzyk, “Fundamental limits of the dispersion of the two-photon absorption cross section,” J. Chem. Phys. 123, 194101 (2005).
    [CrossRef] [PubMed]
  20. J. Pérez-Moreno and M. G. Kuzyk, “A correspondence on organometallic complexes for nonlinear optics. 45. Dispersion of the third-order nonlinear optical properties of triphenylamine-cored alkynylruthenium dendrimers. Increasing the nonlinear optical response by two orders of magnitude,” Adv. Mater. , doi:10.1002/adma.201003421 (published online 7 February 2011).
    [CrossRef] [PubMed]
  21. M. G. Kuzyk and D. S. Watkins, “The effects of geometry on the hyperpolarizability,” J. Chem. Phys. 124, 244104 (2006).
    [CrossRef] [PubMed]
  22. J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Pushing the hyperpolarizability to the limit,” Opt. Lett. 31, 2891–2893 (2006).
    [CrossRef] [PubMed]
  23. J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
    [CrossRef]
  24. J. Pérez-Moreno, Y. Zhao, K. Clays, and M. G. Kuzyk, “Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability,” Opt. Lett. 32, 59–61 (2007).
    [CrossRef]
  25. J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
    [CrossRef] [PubMed]
  26. D. S. Watkins and M. G. Kuzyk, “Optimizing the hyperpolarizability tensor using external electromagnetic fields and nuclear placement,” J. Chem. Phys. 131, 064110 (2009).
    [CrossRef] [PubMed]
  27. M. Wang, X. Hu, D. N. Beratan, and W. Yang, “Designing molecules by optimizing potentials,” J. Am. Chem. Soc. 128, 3228–3232 (2006).
    [CrossRef] [PubMed]
  28. M. C. Kuzyk and M. G. Kuzyk, “Monte Carlo studies of the fundamental limits of the intrinsic hyperpolarizability,” J. Opt. Soc. Am. B 25, 103–110 (2008).
    [CrossRef]
  29. S. Shafei, M. C. Kuzyk, and M. G. Kuzyk, “Monte Carlo studies of the intrinsic second hyperpolarizability,” J. Opt. Soc. Am. B 27, 1849–1856 (2010).
    [CrossRef]
  30. J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, and A. F. Garito, “Symmetry-controlled electron correlation mechanism for third order nonlinear optical properties of conjugated linear chains,” Mol. Cryst. Liq. Cryst. 160, 37–51 (1988).
    [CrossRef]
  31. J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, and A. F. Garito, “Nonlinear optical properties of linear chains and electron-correlation effects,” Phys. Rev. B 38, 1573–1576 (1988).
    [CrossRef]
  32. J. W. Wu, J. R. Heflin, R. A. Norwood, K. Y. Wong, O. Zamani-Khamiri, A. F. Garito, P. Kalyanaraman, and J. Sounik, “Nonlinear-optical processes in lower-dimensional conjugated structures,” J. Opt. Soc. Am. B 6, 707–20 (1989).
    [CrossRef]
  33. S. P. Goldman and G. W. F. Drake, “Relativistic sum rules and integral properties of the Dirac equation,” Phys. Rev. A 25, 2877–2881 (1982).
    [CrossRef]
  34. P. T. Leung and M. L. Rustgi, “Relativistic corrections to Bethe sum rule,” Phys. Rev. A 33, 2827–2829 (1986).
    [CrossRef] [PubMed]
  35. S. M. Cohen, “Aspects of relativistic sum rules,” Adv. Quantum Chem. 46, 241–265 (2004).
    [CrossRef]
  36. S. Keinan, M. J. Therien, D. N. Beratan, and W. T. Yang, “Molecular design of porphyrin-based nonlinear optical materials,” J. Phys. Chem. A 112, 12203–12207 (2008).
    [CrossRef] [PubMed]
  37. J. Pérez-Moreno, I. Asselberghs, Y. Zhao, K. Song, H. Nakanishi, S. Okada, K. Nogi, O.-K. Kim, J. Je, J. Matrai, M. De Mayer, and M. G. Kuzyk, “Combined molecular and supramolecular bottom-up nano-engineering for enhanced nonlinear optical response: experiments, modelling and approaching the fundamental limit,” J. Chem. Phys. 126, 074705 (2007).
    [CrossRef] [PubMed]
  38. M. G. Kuzyk, “Compact sum-over-states expression without dipolar terms for calculating nonlinear susceptibilities,” Phys. Rev. A 72, 053819 (2005).
    [CrossRef]
  39. J. Pérez-Moreno, K. Clays, and M. G. Kuzyk, “A new dipole-free sum-over-states expression for the second hyperpolarizability,” J. Chem. Phys. 128, 084109 (2008).
    [CrossRef] [PubMed]
  40. C. W. Dirk and M. G. Kuzyk, “Missing-state analysis: a method for determining the origin of molecular nonlinear optical properties,” Phys. Rev. A 39, 1219–1226 (1989).
    [CrossRef] [PubMed]

2011

J. Pérez-Moreno and M. G. Kuzyk, “A correspondence on organometallic complexes for nonlinear optics. 45. Dispersion of the third-order nonlinear optical properties of triphenylamine-cored alkynylruthenium dendrimers. Increasing the nonlinear optical response by two orders of magnitude,” Adv. Mater. , doi:10.1002/adma.201003421 (published online 7 February 2011).
[CrossRef] [PubMed]

2010

M. G. Kuzyk, “A birds-eye view of nonlinear-optical processes: unification through scale invariance,” Nonlinear Opt. Quantum Opt. 40, 1–13 (2010).

S. Shafei, M. C. Kuzyk, and M. G. Kuzyk, “Monte Carlo studies of the intrinsic second hyperpolarizability,” J. Opt. Soc. Am. B 27, 1849–1856 (2010).
[CrossRef]

2009

R. Roberts, T. Schwich, T. Corkery, M. Cifuentes, K. Green, J. Farmer, P. Low, T. Marder, M. Samoc, and M. Humphrey, “Organometallic complexes for nonlinear optics. 45. Dispersion of the third-order nonlinear optical properties of triphenylamine-cored alkynylruthenium dendrimers,” Adv. Mater. 21, 2318–2322 (2009).
[CrossRef]

M. G. Kuzyk, “Using fundamental principles to understand and optimize nonlinear-optical materials,” J. Mater. Chem. 19, 7444–7465 (2009).
[CrossRef]

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef] [PubMed]

D. S. Watkins and M. G. Kuzyk, “Optimizing the hyperpolarizability tensor using external electromagnetic fields and nuclear placement,” J. Chem. Phys. 131, 064110 (2009).
[CrossRef] [PubMed]

2008

S. Keinan, M. J. Therien, D. N. Beratan, and W. T. Yang, “Molecular design of porphyrin-based nonlinear optical materials,” J. Phys. Chem. A 112, 12203–12207 (2008).
[CrossRef] [PubMed]

J. Pérez-Moreno, K. Clays, and M. G. Kuzyk, “A new dipole-free sum-over-states expression for the second hyperpolarizability,” J. Chem. Phys. 128, 084109 (2008).
[CrossRef] [PubMed]

J. Zhou and M. G. Kuzyk, “Intrinsic hyperpolarizabilities as a figure of merit for electro-optic molecules,” J. Phys. Chem. C 112, 7978–7982 (2008).
[CrossRef]

M. C. Kuzyk and M. G. Kuzyk, “Monte Carlo studies of the fundamental limits of the intrinsic hyperpolarizability,” J. Opt. Soc. Am. B 25, 103–110 (2008).
[CrossRef]

2007

J. Pérez-Moreno, Y. Zhao, K. Clays, and M. G. Kuzyk, “Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability,” Opt. Lett. 32, 59–61 (2007).
[CrossRef]

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef] [PubMed]

J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
[CrossRef]

J. Pérez-Moreno, I. Asselberghs, Y. Zhao, K. Song, H. Nakanishi, S. Okada, K. Nogi, O.-K. Kim, J. Je, J. Matrai, M. De Mayer, and M. G. Kuzyk, “Combined molecular and supramolecular bottom-up nano-engineering for enhanced nonlinear optical response: experiments, modelling and approaching the fundamental limit,” J. Chem. Phys. 126, 074705 (2007).
[CrossRef] [PubMed]

J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
[CrossRef]

2006

M. Wang, X. Hu, D. N. Beratan, and W. Yang, “Designing molecules by optimizing potentials,” J. Am. Chem. Soc. 128, 3228–3232 (2006).
[CrossRef] [PubMed]

K. Tripathy, J. J. Pérez-Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Errata,” J. Chem. Phys. 125, 079905 (2006).
[CrossRef]

M. G. Kuzyk and D. S. Watkins, “The effects of geometry on the hyperpolarizability,” J. Chem. Phys. 124, 244104 (2006).
[CrossRef] [PubMed]

J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Pushing the hyperpolarizability to the limit,” Opt. Lett. 31, 2891–2893 (2006).
[CrossRef] [PubMed]

2005

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem. Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

J. Pérez-Moreno and M. G. Kuzyk, “Fundamental limits of the dispersion of the two-photon absorption cross section,” J. Chem. Phys. 123, 194101 (2005).
[CrossRef] [PubMed]

M. G. Kuzyk, “Compact sum-over-states expression without dipolar terms for calculating nonlinear susceptibilities,” Phys. Rev. A 72, 053819 (2005).
[CrossRef]

J. C. May, J. H. Lim, I. Biaggio, N. N. P. Moonen, T. Michinobu, and F. Diederich, “Highly efficient third-order optical nonlinearities in donor-substituted cyanoethynylethene molecules,” Opt. Lett. 30, 3057–3059 (2005).
[CrossRef] [PubMed]

2004

S. M. Cohen, “Aspects of relativistic sum rules,” Adv. Quantum Chem. 46, 241–265 (2004).
[CrossRef]

A. D. Slepkov, F. A. Hegmann, S. Eisler, E. Elliot, and R. R. Tykwinski, “The surprising nonlinear optical properties of conjugated polyyne oligomers,” J. Chem. Phys. 120, 6807–6810(2004).
[CrossRef] [PubMed]

Q. Y. Chen, L. Kuang, Z. Y. Wang, and E. H. Sargent, “Cross-linked C-60 polymer breaches the quantum gap,” Nano Lett. 4, 1673–1675 (2004).
[CrossRef]

K. Tripathy, J. Pérez-Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945(2004).
[CrossRef] [PubMed]

2003

M. G. Kuzyk, “Errata,” Phys. Rev. Lett. 90, 039902 (2003).
[CrossRef]

M. G. Kuzyk, “Fundamental limits on two-photon absorption cross-sections,” J. Chem. Phys. 119, 8327–8334 (2003).
[CrossRef]

M. G. Kuzyk, “Errata,” Opt. Lett. 28, 135–135 (2003).
[CrossRef]

2001

M. G. Kuzyk, “Quantum limits of the hyper-Rayleigh scattering susceptibility,” IEEE J. Sel. Top. Quantum Electron. 7, 774–780(2001).
[CrossRef]

2000

M. G. Kuzyk, “Physical limits on electronic nonlinear molecular susceptibilities,” Phys. Rev. Lett. 85, 1218–1221 (2000).
[CrossRef] [PubMed]

M. G. Kuzyk, “Fundamental limits on third-order molecular susceptibilities,” Opt. Lett. 25, 1183–1185 (2000).
[CrossRef]

1989

1988

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, and A. F. Garito, “Symmetry-controlled electron correlation mechanism for third order nonlinear optical properties of conjugated linear chains,” Mol. Cryst. Liq. Cryst. 160, 37–51 (1988).
[CrossRef]

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, and A. F. Garito, “Nonlinear optical properties of linear chains and electron-correlation effects,” Phys. Rev. B 38, 1573–1576 (1988).
[CrossRef]

1986

P. T. Leung and M. L. Rustgi, “Relativistic corrections to Bethe sum rule,” Phys. Rev. A 33, 2827–2829 (1986).
[CrossRef] [PubMed]

1982

S. P. Goldman and G. W. F. Drake, “Relativistic sum rules and integral properties of the Dirac equation,” Phys. Rev. A 25, 2877–2881 (1982).
[CrossRef]

Asselberghs, I.

J. Pérez-Moreno, I. Asselberghs, Y. Zhao, K. Song, H. Nakanishi, S. Okada, K. Nogi, O.-K. Kim, J. Je, J. Matrai, M. De Mayer, and M. G. Kuzyk, “Combined molecular and supramolecular bottom-up nano-engineering for enhanced nonlinear optical response: experiments, modelling and approaching the fundamental limit,” J. Chem. Phys. 126, 074705 (2007).
[CrossRef] [PubMed]

Beratan, D. N.

S. Keinan, M. J. Therien, D. N. Beratan, and W. T. Yang, “Molecular design of porphyrin-based nonlinear optical materials,” J. Phys. Chem. A 112, 12203–12207 (2008).
[CrossRef] [PubMed]

M. Wang, X. Hu, D. N. Beratan, and W. Yang, “Designing molecules by optimizing potentials,” J. Am. Chem. Soc. 128, 3228–3232 (2006).
[CrossRef] [PubMed]

Biaggio, I.

J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
[CrossRef]

J. C. May, J. H. Lim, I. Biaggio, N. N. P. Moonen, T. Michinobu, and F. Diederich, “Highly efficient third-order optical nonlinearities in donor-substituted cyanoethynylethene molecules,” Opt. Lett. 30, 3057–3059 (2005).
[CrossRef] [PubMed]

Brown, E. C.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef] [PubMed]

Bures, F.

J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
[CrossRef]

Cariati, E.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef] [PubMed]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem. Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Chen, Q. Y.

Q. Y. Chen, L. Kuang, Z. Y. Wang, and E. H. Sargent, “Cross-linked C-60 polymer breaches the quantum gap,” Nano Lett. 4, 1673–1675 (2004).
[CrossRef]

Cifuentes, M.

R. Roberts, T. Schwich, T. Corkery, M. Cifuentes, K. Green, J. Farmer, P. Low, T. Marder, M. Samoc, and M. Humphrey, “Organometallic complexes for nonlinear optics. 45. Dispersion of the third-order nonlinear optical properties of triphenylamine-cored alkynylruthenium dendrimers,” Adv. Mater. 21, 2318–2322 (2009).
[CrossRef]

Clays, K.

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef] [PubMed]

J. Pérez-Moreno, K. Clays, and M. G. Kuzyk, “A new dipole-free sum-over-states expression for the second hyperpolarizability,” J. Chem. Phys. 128, 084109 (2008).
[CrossRef] [PubMed]

J. Pérez-Moreno, Y. Zhao, K. Clays, and M. G. Kuzyk, “Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability,” Opt. Lett. 32, 59–61 (2007).
[CrossRef]

K. Tripathy, J. J. Pérez-Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Errata,” J. Chem. Phys. 125, 079905 (2006).
[CrossRef]

K. Tripathy, J. Pérez-Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945(2004).
[CrossRef] [PubMed]

Coe, B. J.

K. Tripathy, J. J. Pérez-Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Errata,” J. Chem. Phys. 125, 079905 (2006).
[CrossRef]

K. Tripathy, J. Pérez-Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945(2004).
[CrossRef] [PubMed]

Cohen, S. M.

S. M. Cohen, “Aspects of relativistic sum rules,” Adv. Quantum Chem. 46, 241–265 (2004).
[CrossRef]

Corkery, T.

R. Roberts, T. Schwich, T. Corkery, M. Cifuentes, K. Green, J. Farmer, P. Low, T. Marder, M. Samoc, and M. Humphrey, “Organometallic complexes for nonlinear optics. 45. Dispersion of the third-order nonlinear optical properties of triphenylamine-cored alkynylruthenium dendrimers,” Adv. Mater. 21, 2318–2322 (2009).
[CrossRef]

De Mayer, M.

J. Pérez-Moreno, I. Asselberghs, Y. Zhao, K. Song, H. Nakanishi, S. Okada, K. Nogi, O.-K. Kim, J. Je, J. Matrai, M. De Mayer, and M. G. Kuzyk, “Combined molecular and supramolecular bottom-up nano-engineering for enhanced nonlinear optical response: experiments, modelling and approaching the fundamental limit,” J. Chem. Phys. 126, 074705 (2007).
[CrossRef] [PubMed]

Diederich, F.

J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
[CrossRef]

J. C. May, J. H. Lim, I. Biaggio, N. N. P. Moonen, T. Michinobu, and F. Diederich, “Highly efficient third-order optical nonlinearities in donor-substituted cyanoethynylethene molecules,” Opt. Lett. 30, 3057–3059 (2005).
[CrossRef] [PubMed]

Dirk, C. W.

C. W. Dirk and M. G. Kuzyk, “Missing-state analysis: a method for determining the origin of molecular nonlinear optical properties,” Phys. Rev. A 39, 1219–1226 (1989).
[CrossRef] [PubMed]

Drake, G. W. F.

S. P. Goldman and G. W. F. Drake, “Relativistic sum rules and integral properties of the Dirac equation,” Phys. Rev. A 25, 2877–2881 (1982).
[CrossRef]

Eisler, S.

A. D. Slepkov, F. A. Hegmann, S. Eisler, E. Elliot, and R. R. Tykwinski, “The surprising nonlinear optical properties of conjugated polyyne oligomers,” J. Chem. Phys. 120, 6807–6810(2004).
[CrossRef] [PubMed]

Elliot, E.

A. D. Slepkov, F. A. Hegmann, S. Eisler, E. Elliot, and R. R. Tykwinski, “The surprising nonlinear optical properties of conjugated polyyne oligomers,” J. Chem. Phys. 120, 6807–6810(2004).
[CrossRef] [PubMed]

Facchetti, A.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
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J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
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J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
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Kang, H.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
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H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem. Int. Ed. 44, 7922–7925 (2005).
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K. Tripathy, J. J. Pérez-Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Errata,” J. Chem. Phys. 125, 079905 (2006).
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K. Tripathy, J. Pérez-Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945(2004).
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J. Pérez-Moreno, I. Asselberghs, Y. Zhao, K. Song, H. Nakanishi, S. Okada, K. Nogi, O.-K. Kim, J. Je, J. Matrai, M. De Mayer, and M. G. Kuzyk, “Combined molecular and supramolecular bottom-up nano-engineering for enhanced nonlinear optical response: experiments, modelling and approaching the fundamental limit,” J. Chem. Phys. 126, 074705 (2007).
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Kuzyk, M. G.

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M. G. Kuzyk, “A birds-eye view of nonlinear-optical processes: unification through scale invariance,” Nonlinear Opt. Quantum Opt. 40, 1–13 (2010).

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
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M. G. Kuzyk, “Using fundamental principles to understand and optimize nonlinear-optical materials,” J. Mater. Chem. 19, 7444–7465 (2009).
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M. C. Kuzyk and M. G. Kuzyk, “Monte Carlo studies of the fundamental limits of the intrinsic hyperpolarizability,” J. Opt. Soc. Am. B 25, 103–110 (2008).
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J. Pérez-Moreno, K. Clays, and M. G. Kuzyk, “A new dipole-free sum-over-states expression for the second hyperpolarizability,” J. Chem. Phys. 128, 084109 (2008).
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J. Pérez-Moreno, I. Asselberghs, Y. Zhao, K. Song, H. Nakanishi, S. Okada, K. Nogi, O.-K. Kim, J. Je, J. Matrai, M. De Mayer, and M. G. Kuzyk, “Combined molecular and supramolecular bottom-up nano-engineering for enhanced nonlinear optical response: experiments, modelling and approaching the fundamental limit,” J. Chem. Phys. 126, 074705 (2007).
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J. Pérez-Moreno, Y. Zhao, K. Clays, and M. G. Kuzyk, “Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability,” Opt. Lett. 32, 59–61 (2007).
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M. G. Kuzyk and D. S. Watkins, “The effects of geometry on the hyperpolarizability,” J. Chem. Phys. 124, 244104 (2006).
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J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Pushing the hyperpolarizability to the limit,” Opt. Lett. 31, 2891–2893 (2006).
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J. Pérez-Moreno and M. G. Kuzyk, “Fundamental limits of the dispersion of the two-photon absorption cross section,” J. Chem. Phys. 123, 194101 (2005).
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M. G. Kuzyk, “Compact sum-over-states expression without dipolar terms for calculating nonlinear susceptibilities,” Phys. Rev. A 72, 053819 (2005).
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K. Tripathy, J. Pérez-Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945(2004).
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H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem. Int. Ed. 44, 7922–7925 (2005).
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H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
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R. Roberts, T. Schwich, T. Corkery, M. Cifuentes, K. Green, J. Farmer, P. Low, T. Marder, M. Samoc, and M. Humphrey, “Organometallic complexes for nonlinear optics. 45. Dispersion of the third-order nonlinear optical properties of triphenylamine-cored alkynylruthenium dendrimers,” Adv. Mater. 21, 2318–2322 (2009).
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H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
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H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem. Int. Ed. 44, 7922–7925 (2005).
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R. Roberts, T. Schwich, T. Corkery, M. Cifuentes, K. Green, J. Farmer, P. Low, T. Marder, M. Samoc, and M. Humphrey, “Organometallic complexes for nonlinear optics. 45. Dispersion of the third-order nonlinear optical properties of triphenylamine-cored alkynylruthenium dendrimers,” Adv. Mater. 21, 2318–2322 (2009).
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H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
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H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem. Int. Ed. 44, 7922–7925 (2005).
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J. Pérez-Moreno, I. Asselberghs, Y. Zhao, K. Song, H. Nakanishi, S. Okada, K. Nogi, O.-K. Kim, J. Je, J. Matrai, M. De Mayer, and M. G. Kuzyk, “Combined molecular and supramolecular bottom-up nano-engineering for enhanced nonlinear optical response: experiments, modelling and approaching the fundamental limit,” J. Chem. Phys. 126, 074705 (2007).
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Moonen, N. N. P.

Nakanishi, H.

J. Pérez-Moreno, I. Asselberghs, Y. Zhao, K. Song, H. Nakanishi, S. Okada, K. Nogi, O.-K. Kim, J. Je, J. Matrai, M. De Mayer, and M. G. Kuzyk, “Combined molecular and supramolecular bottom-up nano-engineering for enhanced nonlinear optical response: experiments, modelling and approaching the fundamental limit,” J. Chem. Phys. 126, 074705 (2007).
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Nogi, K.

J. Pérez-Moreno, I. Asselberghs, Y. Zhao, K. Song, H. Nakanishi, S. Okada, K. Nogi, O.-K. Kim, J. Je, J. Matrai, M. De Mayer, and M. G. Kuzyk, “Combined molecular and supramolecular bottom-up nano-engineering for enhanced nonlinear optical response: experiments, modelling and approaching the fundamental limit,” J. Chem. Phys. 126, 074705 (2007).
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Norwood, R. A.

Okada, S.

J. Pérez-Moreno, I. Asselberghs, Y. Zhao, K. Song, H. Nakanishi, S. Okada, K. Nogi, O.-K. Kim, J. Je, J. Matrai, M. De Mayer, and M. G. Kuzyk, “Combined molecular and supramolecular bottom-up nano-engineering for enhanced nonlinear optical response: experiments, modelling and approaching the fundamental limit,” J. Chem. Phys. 126, 074705 (2007).
[CrossRef] [PubMed]

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J. Pérez-Moreno and M. G. Kuzyk, “A correspondence on organometallic complexes for nonlinear optics. 45. Dispersion of the third-order nonlinear optical properties of triphenylamine-cored alkynylruthenium dendrimers. Increasing the nonlinear optical response by two orders of magnitude,” Adv. Mater. , doi:10.1002/adma.201003421 (published online 7 February 2011).
[CrossRef] [PubMed]

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef] [PubMed]

J. Pérez-Moreno, K. Clays, and M. G. Kuzyk, “A new dipole-free sum-over-states expression for the second hyperpolarizability,” J. Chem. Phys. 128, 084109 (2008).
[CrossRef] [PubMed]

J. Pérez-Moreno, Y. Zhao, K. Clays, and M. G. Kuzyk, “Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability,” Opt. Lett. 32, 59–61 (2007).
[CrossRef]

J. Pérez-Moreno, I. Asselberghs, Y. Zhao, K. Song, H. Nakanishi, S. Okada, K. Nogi, O.-K. Kim, J. Je, J. Matrai, M. De Mayer, and M. G. Kuzyk, “Combined molecular and supramolecular bottom-up nano-engineering for enhanced nonlinear optical response: experiments, modelling and approaching the fundamental limit,” J. Chem. Phys. 126, 074705 (2007).
[CrossRef] [PubMed]

K. Tripathy, J. J. Pérez-Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Errata,” J. Chem. Phys. 125, 079905 (2006).
[CrossRef]

J. Pérez-Moreno and M. G. Kuzyk, “Fundamental limits of the dispersion of the two-photon absorption cross section,” J. Chem. Phys. 123, 194101 (2005).
[CrossRef] [PubMed]

K. Tripathy, J. Pérez-Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945(2004).
[CrossRef] [PubMed]

Qiu, L.

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef] [PubMed]

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H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef] [PubMed]

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H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef] [PubMed]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem. Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Roberts, R.

R. Roberts, T. Schwich, T. Corkery, M. Cifuentes, K. Green, J. Farmer, P. Low, T. Marder, M. Samoc, and M. Humphrey, “Organometallic complexes for nonlinear optics. 45. Dispersion of the third-order nonlinear optical properties of triphenylamine-cored alkynylruthenium dendrimers,” Adv. Mater. 21, 2318–2322 (2009).
[CrossRef]

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P. T. Leung and M. L. Rustgi, “Relativistic corrections to Bethe sum rule,” Phys. Rev. A 33, 2827–2829 (1986).
[CrossRef] [PubMed]

Samoc, M.

R. Roberts, T. Schwich, T. Corkery, M. Cifuentes, K. Green, J. Farmer, P. Low, T. Marder, M. Samoc, and M. Humphrey, “Organometallic complexes for nonlinear optics. 45. Dispersion of the third-order nonlinear optical properties of triphenylamine-cored alkynylruthenium dendrimers,” Adv. Mater. 21, 2318–2322 (2009).
[CrossRef]

Sargent, E. H.

Q. Y. Chen, L. Kuang, Z. Y. Wang, and E. H. Sargent, “Cross-linked C-60 polymer breaches the quantum gap,” Nano Lett. 4, 1673–1675 (2004).
[CrossRef]

Schwich, T.

R. Roberts, T. Schwich, T. Corkery, M. Cifuentes, K. Green, J. Farmer, P. Low, T. Marder, M. Samoc, and M. Humphrey, “Organometallic complexes for nonlinear optics. 45. Dispersion of the third-order nonlinear optical properties of triphenylamine-cored alkynylruthenium dendrimers,” Adv. Mater. 21, 2318–2322 (2009).
[CrossRef]

Shafei, S.

Shen, Y.

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef] [PubMed]

Slepkov, A. D.

A. D. Slepkov, F. A. Hegmann, S. Eisler, E. Elliot, and R. R. Tykwinski, “The surprising nonlinear optical properties of conjugated polyyne oligomers,” J. Chem. Phys. 120, 6807–6810(2004).
[CrossRef] [PubMed]

Song, K.

J. Pérez-Moreno, I. Asselberghs, Y. Zhao, K. Song, H. Nakanishi, S. Okada, K. Nogi, O.-K. Kim, J. Je, J. Matrai, M. De Mayer, and M. G. Kuzyk, “Combined molecular and supramolecular bottom-up nano-engineering for enhanced nonlinear optical response: experiments, modelling and approaching the fundamental limit,” J. Chem. Phys. 126, 074705 (2007).
[CrossRef] [PubMed]

Sounik, J.

Stern, C. L.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef] [PubMed]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem. Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Szafruga, U. B.

J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
[CrossRef]

Therien, M. J.

S. Keinan, M. J. Therien, D. N. Beratan, and W. T. Yang, “Molecular design of porphyrin-based nonlinear optical materials,” J. Phys. Chem. A 112, 12203–12207 (2008).
[CrossRef] [PubMed]

Tripathy, K.

K. Tripathy, J. J. Pérez-Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Errata,” J. Chem. Phys. 125, 079905 (2006).
[CrossRef]

K. Tripathy, J. Pérez-Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945(2004).
[CrossRef] [PubMed]

Tykwinski, R. R.

A. D. Slepkov, F. A. Hegmann, S. Eisler, E. Elliot, and R. R. Tykwinski, “The surprising nonlinear optical properties of conjugated polyyne oligomers,” J. Chem. Phys. 120, 6807–6810(2004).
[CrossRef] [PubMed]

Ugo, R.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef] [PubMed]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem. Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Wang, M.

M. Wang, X. Hu, D. N. Beratan, and W. Yang, “Designing molecules by optimizing potentials,” J. Am. Chem. Soc. 128, 3228–3232 (2006).
[CrossRef] [PubMed]

Wang, Z. Y.

Q. Y. Chen, L. Kuang, Z. Y. Wang, and E. H. Sargent, “Cross-linked C-60 polymer breaches the quantum gap,” Nano Lett. 4, 1673–1675 (2004).
[CrossRef]

Watkins, D. S.

D. S. Watkins and M. G. Kuzyk, “Optimizing the hyperpolarizability tensor using external electromagnetic fields and nuclear placement,” J. Chem. Phys. 131, 064110 (2009).
[CrossRef] [PubMed]

J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
[CrossRef]

J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Pushing the hyperpolarizability to the limit,” Opt. Lett. 31, 2891–2893 (2006).
[CrossRef] [PubMed]

M. G. Kuzyk and D. S. Watkins, “The effects of geometry on the hyperpolarizability,” J. Chem. Phys. 124, 244104 (2006).
[CrossRef] [PubMed]

Wong, K. Y.

J. W. Wu, J. R. Heflin, R. A. Norwood, K. Y. Wong, O. Zamani-Khamiri, A. F. Garito, P. Kalyanaraman, and J. Sounik, “Nonlinear-optical processes in lower-dimensional conjugated structures,” J. Opt. Soc. Am. B 6, 707–20 (1989).
[CrossRef]

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, and A. F. Garito, “Symmetry-controlled electron correlation mechanism for third order nonlinear optical properties of conjugated linear chains,” Mol. Cryst. Liq. Cryst. 160, 37–51 (1988).
[CrossRef]

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, and A. F. Garito, “Nonlinear optical properties of linear chains and electron-correlation effects,” Phys. Rev. B 38, 1573–1576 (1988).
[CrossRef]

Wu, J. W.

Yang, W.

M. Wang, X. Hu, D. N. Beratan, and W. Yang, “Designing molecules by optimizing potentials,” J. Am. Chem. Soc. 128, 3228–3232 (2006).
[CrossRef] [PubMed]

Yang, W. T.

S. Keinan, M. J. Therien, D. N. Beratan, and W. T. Yang, “Molecular design of porphyrin-based nonlinear optical materials,” J. Phys. Chem. A 112, 12203–12207 (2008).
[CrossRef] [PubMed]

Yang, Y.

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem. Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Zamani-Khamiri, O.

J. W. Wu, J. R. Heflin, R. A. Norwood, K. Y. Wong, O. Zamani-Khamiri, A. F. Garito, P. Kalyanaraman, and J. Sounik, “Nonlinear-optical processes in lower-dimensional conjugated structures,” J. Opt. Soc. Am. B 6, 707–20 (1989).
[CrossRef]

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, and A. F. Garito, “Symmetry-controlled electron correlation mechanism for third order nonlinear optical properties of conjugated linear chains,” Mol. Cryst. Liq. Cryst. 160, 37–51 (1988).
[CrossRef]

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, and A. F. Garito, “Nonlinear optical properties of linear chains and electron-correlation effects,” Phys. Rev. B 38, 1573–1576 (1988).
[CrossRef]

Zhao, Y.

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef] [PubMed]

J. Pérez-Moreno, I. Asselberghs, Y. Zhao, K. Song, H. Nakanishi, S. Okada, K. Nogi, O.-K. Kim, J. Je, J. Matrai, M. De Mayer, and M. G. Kuzyk, “Combined molecular and supramolecular bottom-up nano-engineering for enhanced nonlinear optical response: experiments, modelling and approaching the fundamental limit,” J. Chem. Phys. 126, 074705 (2007).
[CrossRef] [PubMed]

J. Pérez-Moreno, Y. Zhao, K. Clays, and M. G. Kuzyk, “Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability,” Opt. Lett. 32, 59–61 (2007).
[CrossRef]

Zhou, J.

J. Zhou and M. G. Kuzyk, “Intrinsic hyperpolarizabilities as a figure of merit for electro-optic molecules,” J. Phys. Chem. C 112, 7978–7982 (2008).
[CrossRef]

J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
[CrossRef]

J. Zhou, M. G. Kuzyk, and D. S. Watkins, “Pushing the hyperpolarizability to the limit,” Opt. Lett. 31, 2891–2893 (2006).
[CrossRef] [PubMed]

Zhu, P.

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem. Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Zuccaccia, C.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef] [PubMed]

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem. Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Adv. Mater.

R. Roberts, T. Schwich, T. Corkery, M. Cifuentes, K. Green, J. Farmer, P. Low, T. Marder, M. Samoc, and M. Humphrey, “Organometallic complexes for nonlinear optics. 45. Dispersion of the third-order nonlinear optical properties of triphenylamine-cored alkynylruthenium dendrimers,” Adv. Mater. 21, 2318–2322 (2009).
[CrossRef]

J. Pérez-Moreno and M. G. Kuzyk, “A correspondence on organometallic complexes for nonlinear optics. 45. Dispersion of the third-order nonlinear optical properties of triphenylamine-cored alkynylruthenium dendrimers. Increasing the nonlinear optical response by two orders of magnitude,” Adv. Mater. , doi:10.1002/adma.201003421 (published online 7 February 2011).
[CrossRef] [PubMed]

Adv. Quantum Chem.

S. M. Cohen, “Aspects of relativistic sum rules,” Adv. Quantum Chem. 46, 241–265 (2004).
[CrossRef]

Angew. Chem. Int. Ed.

H. Kang, A. Facchetti, P. Zhu, H. Jiang, Y. Yang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. Liu, S. T. Ho, and T. J. Marks, “Exceptional molecular hyperpolarizabilities in twisted π-electron system chromophores,” Angew. Chem. Int. Ed. 44, 7922–7925 (2005).
[CrossRef]

Appl. Phys. Lett.

J. C. May, I. Biaggio, F. Bures, and F. Diederich, “Extended conjugation and donor-acceptor substitution to improve the third-order optical nonlinearity of small molecules,” Appl. Phys. Lett. 90, 251106 (2007).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

M. G. Kuzyk, “Quantum limits of the hyper-Rayleigh scattering susceptibility,” IEEE J. Sel. Top. Quantum Electron. 7, 774–780(2001).
[CrossRef]

J. Am. Chem. Soc.

H. Kang, A. Facchetti, H. Jiang, E. Cariati, S. Righetto, R. Ugo, C. Zuccaccia, A. Macchioni, C. L. Stern, Z. F. Liu, S. T. Ho, E. C. Brown, M. A. Ratner, and T. J. Marks, “Ultralarge hyperpolarizability twisted π-electron system electro-optic chromophores: synthesis, solid-state and solution-phase structural characteristics, electronic structures, linear and nonlinear optical properties, and computational studies,” J. Am. Chem. Soc. 129, 3267–3286 (2007).
[CrossRef] [PubMed]

J. Pérez-Moreno, Y. Zhao, K. Clays, M. G. Kuzyk, Y. Shen, L. Qiu, J. Hao, and K. Guo, “Modulated conjugation as a means of improving the intrinsic hyperpolarizability,” J. Am. Chem. Soc. 131, 5084–5093 (2009).
[CrossRef] [PubMed]

M. Wang, X. Hu, D. N. Beratan, and W. Yang, “Designing molecules by optimizing potentials,” J. Am. Chem. Soc. 128, 3228–3232 (2006).
[CrossRef] [PubMed]

J. Chem. Phys.

J. Pérez-Moreno, I. Asselberghs, Y. Zhao, K. Song, H. Nakanishi, S. Okada, K. Nogi, O.-K. Kim, J. Je, J. Matrai, M. De Mayer, and M. G. Kuzyk, “Combined molecular and supramolecular bottom-up nano-engineering for enhanced nonlinear optical response: experiments, modelling and approaching the fundamental limit,” J. Chem. Phys. 126, 074705 (2007).
[CrossRef] [PubMed]

J. Pérez-Moreno, K. Clays, and M. G. Kuzyk, “A new dipole-free sum-over-states expression for the second hyperpolarizability,” J. Chem. Phys. 128, 084109 (2008).
[CrossRef] [PubMed]

D. S. Watkins and M. G. Kuzyk, “Optimizing the hyperpolarizability tensor using external electromagnetic fields and nuclear placement,” J. Chem. Phys. 131, 064110 (2009).
[CrossRef] [PubMed]

M. G. Kuzyk and D. S. Watkins, “The effects of geometry on the hyperpolarizability,” J. Chem. Phys. 124, 244104 (2006).
[CrossRef] [PubMed]

M. G. Kuzyk, “Fundamental limits on two-photon absorption cross-sections,” J. Chem. Phys. 119, 8327–8334 (2003).
[CrossRef]

J. Pérez-Moreno and M. G. Kuzyk, “Fundamental limits of the dispersion of the two-photon absorption cross section,” J. Chem. Phys. 123, 194101 (2005).
[CrossRef] [PubMed]

K. Tripathy, J. Pérez-Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Why hyperpolarizabilities fall short of the fundamental quantum limits,” J. Chem. Phys. 121, 7932–7945(2004).
[CrossRef] [PubMed]

K. Tripathy, J. J. Pérez-Moreno, M. G. Kuzyk, B. J. Coe, K. Clays, and A. M. Kelley, “Errata,” J. Chem. Phys. 125, 079905 (2006).
[CrossRef]

A. D. Slepkov, F. A. Hegmann, S. Eisler, E. Elliot, and R. R. Tykwinski, “The surprising nonlinear optical properties of conjugated polyyne oligomers,” J. Chem. Phys. 120, 6807–6810(2004).
[CrossRef] [PubMed]

J. Mater. Chem.

M. G. Kuzyk, “Using fundamental principles to understand and optimize nonlinear-optical materials,” J. Mater. Chem. 19, 7444–7465 (2009).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. Chem. A

S. Keinan, M. J. Therien, D. N. Beratan, and W. T. Yang, “Molecular design of porphyrin-based nonlinear optical materials,” J. Phys. Chem. A 112, 12203–12207 (2008).
[CrossRef] [PubMed]

J. Phys. Chem. C

J. Zhou and M. G. Kuzyk, “Intrinsic hyperpolarizabilities as a figure of merit for electro-optic molecules,” J. Phys. Chem. C 112, 7978–7982 (2008).
[CrossRef]

Mol. Cryst. Liq. Cryst.

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, and A. F. Garito, “Symmetry-controlled electron correlation mechanism for third order nonlinear optical properties of conjugated linear chains,” Mol. Cryst. Liq. Cryst. 160, 37–51 (1988).
[CrossRef]

Nano Lett.

Q. Y. Chen, L. Kuang, Z. Y. Wang, and E. H. Sargent, “Cross-linked C-60 polymer breaches the quantum gap,” Nano Lett. 4, 1673–1675 (2004).
[CrossRef]

Nonlinear Opt. Quantum Opt.

M. G. Kuzyk, “A birds-eye view of nonlinear-optical processes: unification through scale invariance,” Nonlinear Opt. Quantum Opt. 40, 1–13 (2010).

Opt. Lett.

Phys. Rev. A

C. W. Dirk and M. G. Kuzyk, “Missing-state analysis: a method for determining the origin of molecular nonlinear optical properties,” Phys. Rev. A 39, 1219–1226 (1989).
[CrossRef] [PubMed]

M. G. Kuzyk, “Compact sum-over-states expression without dipolar terms for calculating nonlinear susceptibilities,” Phys. Rev. A 72, 053819 (2005).
[CrossRef]

J. Zhou, U. B. Szafruga, D. S. Watkins, and M. G. Kuzyk, “Optimizing potential energy functions for maximal intrinsic hyperpolarizability,” Phys. Rev. A 76, 053831 (2007).
[CrossRef]

S. P. Goldman and G. W. F. Drake, “Relativistic sum rules and integral properties of the Dirac equation,” Phys. Rev. A 25, 2877–2881 (1982).
[CrossRef]

P. T. Leung and M. L. Rustgi, “Relativistic corrections to Bethe sum rule,” Phys. Rev. A 33, 2827–2829 (1986).
[CrossRef] [PubMed]

Phys. Rev. B

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, and A. F. Garito, “Nonlinear optical properties of linear chains and electron-correlation effects,” Phys. Rev. B 38, 1573–1576 (1988).
[CrossRef]

Phys. Rev. Lett.

M. G. Kuzyk, “Physical limits on electronic nonlinear molecular susceptibilities,” Phys. Rev. Lett. 85, 1218–1221 (2000).
[CrossRef] [PubMed]

M. G. Kuzyk, “Errata,” Phys. Rev. Lett. 90, 039902 (2003).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Distribution of β int for energy function E j exp ( j ) .

Fig. 2
Fig. 2

Distribution of γ int for energy function E j exp ( j ) .

Fig. 3
Fig. 3

Distribution of β int as a function of the number of states for several different energy functions. The vertical dashed lines represent f ( E ) for that energy function.

Fig. 4
Fig. 4

β n m int for the energy class j 2 when β int = 0.284 .

Fig. 5
Fig. 5

Density plots from one million Monte Carlo runs of β int as a function of X for several energy classes of a 20-state model. The dashed lines represent ± f ( E ) . Red, blue, and green colors correspond to the β int values for which 3, 4 to 6, and 7 + states dominate the nonlinear response, respectively. The black solid curve represents a plot of ± f ( E ) G ( X ) for E fixed by the energy class and as a function of X.

Fig. 6
Fig. 6

Distribution of the second hyperpolarizability for energy class j 3 .

Fig. 7
Fig. 7

Distribution of γ int with energy for several different energy functions. The vertical dashed lines represent the energy function f γ ( E ) .

Fig. 8
Fig. 8

γ int as a function of X for several energy classes using a 20-state model. Dashed lines represent F γ ( E ) . The black solid curve specifies the limit defined by the sum-rule-constrained three- level model.

Fig. 9
Fig. 9

Distribution of β int for the energy class j 2 (top) and j 3 (bottom).

Tables (2)

Tables Icon

Table 1 Summary of the Properties of the Hyperpolarizability for Various Energy Functions When the Hyperpolarizability is Small or Near the Limit

Tables Icon

Table 2 Summary of the Properties of the Second Hyperpolarizability for a Sampling of Energy Functions When the Second Hyperpolarizability is Small or Near the Limit

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

β max = 3 1 / 4 ( e m ) 3 ( N 3 / 2 E 10 7 / 2 ) ,
( e m ) 4 N 2 E 10 5 γ 0 4 ( e m ) 4 N 2 E 10 5 γ max .
β int = β β max and γ int = γ γ max ,
n = 0 [ E n 1 2 ( E m + E p ) ] x m n x n p = 2 N 2 m δ m p ,
n = 0 [ e n 1 2 ( e m + e p ) ] ξ m n ξ n p = δ m p ,
ξ i j = x i j | x 01 max | ,
| x 01 max | 2 = 2 N 2 m E 10 .
E s = f ( s ) .
E j = 1 j 1 j + 1 + 1.
e 10 | ξ 10 | 2 + e 20 | ξ 20 | 2 + e 30 | ξ 30 | 2 + + e n 0 | ξ n 0 | 2 = 1.
n = 2 e n 0 ξ n 0 2 = 1 e 10 ξ 10 2 ,
ξ 20 2 ( 1 e 1 ξ 10 2 ) / e 20 .
ξ 20 = r ( 1 e 1 ξ 10 2 ) / e 20 .
ξ i j = ξ j i .
β = 3 e 3 n , m x 0 n x n m x m 0 ( 1 E n 0 E m 0 2 E m 0 E n 0 E n 0 2 E m 0 ) ,
γ = 1 8 ( 2 n m n l n { ( 2 E m 0 E n 0 ) ( 2 E l 0 E n 0 ) E n 0 5 ( 2 E l 0 E n 0 ) E m 0 E n 0 3 } x 0 m x m n x n l x l 0 + 2 n m n l m { 1 E l 0 E m 0 E n 0 ( 2 E l 0 E m 0 ) E m 0 3 E n 0 } x 0 l x l m x m n x n 0 m n { 1 E m 0 2 E n 0 + 1 E n 0 2 E m 0 } x 0 m 2 x 0 n 2 ) .
β = 6 2 3 e 3 | x 10 MAX | 3 E 10 2 G ( X ) f ( E ) = β 0 G ( X ) f ( E ) ,
f ( E ) = ( 1 E ) 3 / 2 ( E 2 + 3 2 E + 1 ) ,
G ( X ) = 3 4 X 3 2 ( 1 X 4 ) ,
β = n , m β n m .
β int = G ( X ) f ( E ) = 3 4 ( 1 E ) 3 / 2 ( E 2 + 3 2 E + 1 ) X 3 2 ( 1 X 4 ) .
γ x x x x off = e 4 4 m 2 E 10 5 G γ ( E , X ) ,
G γ ( E , X ) = 4 5 ( E 1 ) 2 ( E + 1 ) ( E 2 + E + 1 ) X 4 2 ( E 2 1 ) E 3 X 2 ( E 3 + E + 3 ) E 2 .
γ int = γ x x x x off γ max = G γ ( E , X ) 4 .
X 0 ( 1 ) ( E ) = 0 and X 0 ( 2 ) ( E ) = ± E 3 / 2 5 ( 1 E 3 ) .
f γ ( E ) G ( E , X 0 ( 2 ) ( E ) ) 4 = 1 20 ( 19 14 E 2 6 E 3 4 E 5 + 1 + E 1 + E + E 2 ) .

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